Accurate determination of lattice parameters based on Niggli reduced cell theory by using digitized electron diffraction micrograph. (May 2017) - Yang, Yi; Cai, Canying; Lin, Jianguo; Gong, Lunjun; Yang, Qibin
Highlights: Suitable to determinate lattice constants of a known or an unknown crystal. Measured angles directly on the electron micrographs instead of a double tilt holder. Used digitized micrographs and the least square method to optimize parameters. Enhanced the accuracy of lattice constant measurement obviously. Abstract: In this paper, we used Niggli reduced cell theory to determine lattice constants of a micro/nano crystal by using electron diffraction patterns. The Niggli reduced cell method enhanced the accuracy of lattice constant measurement obviously, because the lengths and the angles of lattice vectors of a primitive cell can be measured directly on the electron micrographs instead of a double tilt holder. With the aid of digitized algorithm and least square optimization by using three digitized micrographs, a valid reciprocal Niggli reduced cell number can be obtained. Thus a reciprocal and real Bravais lattices are acquired. The results of three examples, i.e., Mg4 Zn7, an unknown phase (Precipitate phase in nickel-base superalloy) and Ba4 Ti13 O30 showed that the maximum errors are 1.6% for lengths and are 0.3% for angles.